Exam 2: Right Triangle Trigonometry

Two people decide to estimate the height of a flag pole. One person positions himself due north of the pole and the other person stands due east of the pole. If the two people are the same distance from the pole and 27 feet from each other, find the height of the pole if the angle of elevation from the ground at each person's position to the top of the pole is 54° (see the figure). Round to the nearest feet. ​ ​

Solve the following problem. Be sure to make a diagram of the situation with all the given information labeled. A tree on one side of a river is due west of a rock on the other side of the river. From a stake 21 yards north of the rock, the bearing of the tree is S 18.5º W. How far is it from the rock to the tree? Apply the rules regarding the use of significant digits when determining your answer. Distance between rock and tree = __________ yd

Add. (34°46')+ (29°24')_____°_____'

Work each of the following problems on your calculator. Do not write down or round off any intermediate answers.  = __________  =  __________  =  __________  =  __________

Refer to right triangle ABC with . If  and  cm, find b . Round the answer to the nearest whole number. ​

Solve the following problem. Be sure to make a diagram of the situation with all the given information labeled. How long should an escalator be if it is to make an angle of 26° with the floor and carry people a vertical distance of 18 feet between floors? Apply the rules regarding the use of significant digits when determining your answer. Round to the nearest foot. Length of escalator = __________ ft

Solve the problem. Be sure to make a diagram of the situation with all the given information labeled. A man wandering in the desert walks 2.5  miles in the direction  . He then turns  90° and walks 3.3 miles in the direction  . At that time, how far is he from his starting point, and what is his bearing from his starting point? Round the distance to one decimal place and the angle to the whole number. ​ ​

Find θ  if θ  is between 0° and 90°. Round your answer to the nearest tenth of a degree. cot  θ = 0.8536 ​

For the expression that follows, replace x with 30°, and then simplify as much as possible. ​

Draw a vector representing the following velocity. 50 mph due west ​

Danny and Stacey have gone from the swing to the slide at the park. The slide is inclined at an angle . Danny weighs 39.0 pounds. He is sitting in a cardboard box with a piece of wax paper on the bottom. Stacey is at the top of the slide holding on to the cardboard box. Find the magnitude of the force Stacey must pull with, in order to keep Danny from sliding down the slide. (We are assuming that the wax paper makes the slide into a frictionless surface, so that the only force keeping Danny from sliding is the force with which Stacey pulls.)​    ​

Suppose each edge of the cube shown in the figure is 3 inches long. Find the sine and cosine of the angle formed by diagonals GB and 0 GD . ​

The magnitude of the horizontal and vertical vector components  and  of vector V are given. Find the magnitude of V . Apply the rules regarding the use of significant digits when determining your answers. ​ __________

The figure shows a simplified model of the first Ferris wheel. The radius of the first Ferris wheel was 125 feet, and the distance from the ground to the bottom of the wheel was 14 feet. If  is the central angle formed as a rider moves from position  to position , find the rider's height above the ground h when  is . Round the answer to the nearest whole number. ​

Use a calculator to find the following. Round your answer to four places past the decimal point. sec 60°48'

A ship is  off course. If the ship is traveling at 18 miles per hour, how far off course will it be after 4 hours? Apply the rules regarding the use of significant digits when determining your answer. __________ mi

A person standing 150 centimeters from a mirror notices that the angle of depression from his eyes to the bottom of the mirror is 14°, while the angle of elevation to the top of the mirror is 12°. Find the vertical dimension of the mirror (see the figure). Round to the nearest degree. ​

Vector V with magnitude  forms an angle with the positive x -axis. Give the magnitude of the horizontal and vertical vector components of V , namely  and , respectively. ,  ​

Find the exact value of . ​

The circle in the figure has a radius of r and center at C . The distance from A to B is x . ​ If  and , find r . Round the answer to the nearest whole number. ​